From Fig. REF , one can reach many conclusions. A PRHM scenario
is most likely possible, where the radiative corrections can give
rise to the Higgs mass and simultaneously push the scalar mixing to
be in agreement with the total Higgs strength bound [1]}.
For instance, for heavy scalar masses below \(3~\mathrm {TeV}\) , the
one-loop quartic couplings \(\lambda _{H}^{1-\ell }\)  and \(\omega ^{1-\ell }\) 
are not practically constrained by the perturbativity since they are
lying in the ranges \([0.07,2.5]\)  and \([-1,2]\) , respectively. However,
the singlet one-loop quartic coupling \(10^{-5}<\lambda _{\phi }^{1-\ell }\le 4\pi \) ,
together with the previous requirements make the singlet scalar VEV
lies in the range \(600~\mathrm {GeV}<x<100~\mathrm {TeV}\) . Here, the
fact that the heavy scalar is barely constrained by the recent RUN-II
measurements of ATLAS with 139 \(\mathrm {fb}^{-1}\)  [2]}, [3]}, [4]},
and CMS with 137 \(\mathrm {fb}^{-1}\)  [5]}, makes this scenario
within the reach of the coming analysis.
